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Biostatistics 3:289-298 (2002)
© 2002 Oxford University Press

Parametric and semiparametric approaches to testing for seasonal trend in serial count data

Sally Hunsberger, Paul S. Albert, Dean A. Follmann and Edward Suh

Sally Hunsberger. National Cancer Institute, 6130 Executive Blvd. MSC 7434, Bethesda, MD 20892-7434, USA hunsber{at}helix.nih.gov
Paul S. Albert. National Cancer Institute, 6130 Executive Blvd. MSC 7434, Bethesda, MD 20892-7434, USA
Dean A. Follmann. National Heart, Lung, and Blood Institute, 2 Rockledge Center, MSC 7938, Bethesda, MD 20892-7938, USA
Edward Suh. Center for Information Technology, NIH, Building 12, room 2033, Bethesda, MD 20892, USA

We present two tests for seasonal trend in monthly incidence data. The first approach uses a penalized likelihood to choose the number of harmonic terms to include in a parametric harmonic model (which includes time trends and autogression as well as seasonal harmonic terms) and then tests for seasonality using a parametric bootstrap test. The second approach uses a semiparametric regression model to test for seasonal trend. In the semiparametric model, the seasonal pattern is modeled nonparametrically, parametric terms are included for autoregressive effects and a linear time trend, and a parametric bootstrap test is used to test for seasonality. For both procedures, a null distribution is generated under a null Poisson model with time trends and autoregression parameters.We apply the methods to skin melanoma incidence rates collected by the surveillance, epidemiology, and end results (SEER) program of the National Cancer Institute, and perform simulation studies to evaluate the type I error rate and power for the two procedures. These simulations suggest that both procedures are alpha-level procedures. In addition, the harmonic model/bootstrap test had similar or larger power than the semiparametric model/bootstrap test for a wide range of alternatives, and the harmonic model/bootstrap test is much easier to implement. Thus, we recommend the harmonic model/bootstrap test for the analysis of seasonal incidence data.

Keywords: Harmonic models; Incidence data; Parametric bootstrap test; Smoothing; Time series count data


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